Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising
For online advertising platforms using auto-bidding, this work provides theoretical guarantees on the efficiency of proportional mechanisms, with the modified version significantly improving upon the existing PoA barrier.
The paper establishes a tight price of anarchy (PoA) bound of 2 for the standard proportional mechanism in auto-bidding advertising, and introduces a modified version that achieves a PoA bound of 1 + O(1)/(n-1), approaching full efficiency as the number of agents increases.
The rise of automated bidding strategies in online advertising presents new challenges in designing and analyzing efficient auction mechanisms. In this paper, we focus on proportional mechanisms within the context of auto-bidding and study the efficiency of pure Nash equilibria, specifically the price of anarchy (PoA), under the liquid welfare objective. We first establish a tight PoA bound of 2 for the standard proportional mechanism. Next, we introduce a modified version with an alternative payment scheme that achieves a PoA bound of $1 + \frac{O(1)}{n-1}$ where $n \geq 2$ denotes the number of bidding agents. This improvement surpasses the existing PoA barrier of 2 and approaches full efficiency as the number of agents increases. Our methodology leverages duality and the Karush-Kuhn-Tucker (KKT) conditions from linear and convex programming. Despite its conceptual simplicity, our approach proves powerful and may offer broader applications for establishing PoA bounds.